Pawlett opened the scoring shortly before the break, with Jack heading the second 20 minutes from time.
Although Killie created some early chances, it was Aberdeen’s Niall McGinn who came closest during the opening 30 minutes at Rugby Park where he struck the bar from the edge of the box.
Tope Obadeyi headed over for Killie before the Dons broke the deadlock on the break.
With the first half coming to a close, Jonny Hayes raced clear to release Pawlett who lashed the ball into the top left hand corner of the net from a tight angle.
Manuel Pascali came close to an equaliser but headed wide from close range before Aberdeen added a second.
With 70 minutes on the clock, Jack netted from inside the six-yard box nodding home McGinn’s assist.